I Why is there no consensus about the meaning of probability in MWI?

[pines-demon]

"Valid" in what sense?

It provides you a distribution of outcomes that can be compared with the predictions of usual QM. It may match or not match the predictions depending on what you assume are the weights (again in Carroll's sense of weights).

 

[kered rettop]

Sure it is unconvicing if you wanted to derive the Born rule from MWI. Yet it works as a valid way to get a distribution of outcomes. That's all the point I was trying to make. If you want to avoid calling that "probability" I may agree but I hope it answers the question of OP.

It does not!

 

[pines-demon]

It does not!

In QM interpretations, one can only hope

 

[PeterDonis]

It provides you a distribution of outcomes that can be compared with the predictions of usual QM.

No, it doesn't. The "distribution of outcomes" that we measure (in the context of the MWI) is relative frequencies in one world. It is not the relative weightings of different worlds in the wave function. So any claim about "distribution" that involves relative weightings is irrelevant to comparing our measurements with predictions. I pointed this out a while ago in the thread.

 

[pines-demon]

No, it doesn't. The "distribution of outcomes" that we measure (in the context of the MWI) is relative frequencies in one world. It is not the relative weightings of different worlds in the wave function. So any claim about "distribution" that involves relative weightings is irrelevant to comparing our measurements with predictions. I pointed this out a while ago in the thread.

I know that you are unconvinced but see it this way, if they repeat the experiment many times, for most observers at the end of the branch in a given world, both their past branch frequencies and the weights for the different branches for a given future measurement will agree.

 

[kered rettop]

It provides you a distribution of outcomes that can be compared with the predictions of usual QM.

Exactly. If it looks like probability and quacks like probabiity then it...
... isn't probability, duh!

It may match or not match the predictions depending on what you assume are the weights (again in Carroll's sense of weights).

Well, there shouldn't be any assumption, other than that the probabilities are equal. The thing is - and I think I may have to set up a hotkey to write this, it comes up so often - to derive a probability rule using counting, you have to add the microstates i.e. their amplitude vectors, and add the unknown but equal probabilities. It's not hard. If the microstates arise because of decoherence, they are orthogonal and the Born Rule jumps right out. Carroll's psuedo-branches are not orthogonal, in fact they are parallel. But the outcomes are not independent, they are 100% correllated. You have to use the rule for combining correlated probabilities. And that's assuming you can find a meaning for probability that includes psuedo-branches.

 

[PeterDonis]

see it this way

The argument you are making here has been made in the literature by multiple people, going back, IIRC, some decades. I am not the only one who is not convinced by it. In any case, it is not something we are going to resolve here. Putting the various viewpoints on record here is fine, but we should not expect to actually reach a resolution when the community as a whole has not done so despite discussing this for far longer than we have here.

 

[pines-demon]

The argument you are making here has been made in the literature by multiple people, going back, IIRC, some decades. I am not the only one who is not convinced by it. In any case, it is not something we are going to resolve here. Putting the various viewpoints on record here is fine, but we should not expect to actually reach a resolution when the community as a whole has not done so despite discussing this for far longer than we have here.

I was trying to contest the general idea that probabilities cannot be defined. Putting that term probability aside, there are proposals to do get different distributions that can be compared with usual QM. This last part that does not seem to be a huge point of disagreement between the advocates of MWI. What seems to be a problem is if those proposals derive the Born rule (I am far from being the only one that has arrived to this conclusion here). Anyway, outside advocates of MWI, I do agree that sources disagree in many things.

 

[pines-demon]

Well, there shouldn't be any assumption, other than that the probabilities are equal. The thing is - and I think I may have to set up a hotkey to write this, it comes up so often - to derive a probability rule using counting, you have to add the microstates i.e. their amplitude vectors, and add the unknown but equal probabilities. It's not hard. If the microstates arise because of decoherence, they are orthogonal and the Born Rule jumps right out. Carroll's psuedo-branches are not orthogonal, in fact they are parallel. But the outcomes are not independent, they are 100% correllated. You have to use the rule for combining correlated probabilities. And that's assuming you can find a meaning for probability that includes psuedo-branches.

Not sure I am following. I will answer to a few things. As I read it from the pdf, I think the pseudo-branches are indeed orthogonal (do not ask me to justify that!). I am also avoiding to discuss "probabilities" as it seems to convey a specific nuance that I have not been able to narrow down in this conversation.

 

[PeterDonis]

I was trying to contest the general idea that probabilities cannot be defined.

Yes, and as I said, that debate has been ongoing in the literature for decades now. Your point of view certainly has proponents in the literature, but it also has opponents. The issue is still open.

 

[PeterDonis]

s I read it from the pdf, I think the pseudo-branches are indeed orthogonal

No, they're not, because they are all associated with the same outcome (and in fact "they" are just one actual branch, which can't possibly be orthogonal to itself--that's mathematically impossible).

 

[PeterDonis]

I am also avoiding to discuss "probabilities"

Then I am very confused about why you are even posting in this thread, which, as its title explicitly says, is about the meaning of probability in the MWI.

 

[pines-demon]

Yes, and as I said, that debate has been ongoing in the literature for decades now. Your point of view certainly has proponents in the literature, but it also has opponents. The issue is still open.

Sure but that does not say much, that's why we are exploring those issues.

No, they're not, because they are all associated with the same outcome (and in fact "they" are just one actual branch, which can't possibly be orthogonal to itself--that's mathematically impossible).

Read the pdf, see the probabilities that they get and make you own mind about the orthogonality. These seem to be different branches with similar results. Postulate a hidden quantum number if you will, again it is worked out to reobtain the Born rule.

Then I am very confused about why you are even posting in this thread, which, as its title explicitly says, is about the meaning of probability in the MWI.

I have explained what I meant by it, that is to provide some measure that can be compared with QM. I just trying to formulate something pragmatic, I do not want to enter into these ontic-epistemic debates just by saying the term, I leave that to you.

 

[PeterDonis]

Read the pdf

I have. Its argument has, again, been made in the literature multiple times over decades, and has not resolved the issue (and, as I've said, I don't find it convincing). The reference is given and readers can make up their own minds.

 

[pines-demon]

I have. Its argument has, again, been made in the literature multiple times over decades, and has not resolved the issue (and, as I've said, I don't find it convincing). The reference is given and readers can make up their own minds.

To be clear I am not necessarily inviting you to adhere to it. In this specific exchange I was just trying to clarify a remark by another user related to the paper. Let us not dig too much into the intricacies of the paper.

 

[jbergman]

Yes. But that doesn't mean "we" only observe one world, because "we" are in every world, and the "we" in every world believe that "our" observations are of only one world.

You smuggled a lot of hidden assumptions in this comment, i.e., that we are a single entity after branching.

I know Carroll doesn't espouse this view and instead argues that after branching we are effectively different agents. If you take the point of view you are espousing then there is only the wave function. But as emergent concepts in the classical realm, me and another version of me on a different branch are completely different entities, IMO. This can be made more precise by appealing to decoherence.

 

[PeterDonis]

that we are a single entity after branching

I made no such assumption. In at least one other post (not in response to you) I acknowledged that after the branching, each "we" is different to the extent that "we" have observed a different measurement outcome. I also said that no "we" is privileged over any other; they are all on the same footing and they all have the same "we" before branching in their past. When I talked about the "we" in every world, in what you quoted, that was all I meant.

If you take the point of view you are espousing

I'm not. See above.

there is only the wave function.

There is only the wave function in the MWI. That and the dynamics of the wave function always being unitary (no collapse) are the MWI's primary features. There isn't some other version of the MWI where there is something else in addition to the wave function. The wave function is all there is in the MWI.

me and another version of me on a different branch are completely different entities, IMO. This can be made more precise by appealing to decoherence.

Sure, decoherence is what defines "branching" in the MWI (more precisely, it cleared up what used to be a serious missing piece of the MWI, namely what did define "branching"). That doesn't contradict anything I said above or in my previous posts.

 

[kered rettop]

Done.

It's still there!

 

[kered rettop]

Yes, which I find unconvincing, to say the least. There are no "pseudo-worlds" in the math, and the math is supposed to be the ultimate basis for any interpretation.

I kind of agree except I would say that they cannot be treated the same way as worlds in a world-counting derivation of the Born Rule. Therefore either Carroll isn't doing that, or he has made a giant mistake, or my assertion is wrong.

 

[pines-demon]

I kind of agree except I would say that they cannot be treated the same way as worlds in a world-counting derivation of the Born Rule. Therefore either Carroll isn't doing that, or he has made a giant mistake, or my assertion is wrong.

Nobody is denying that it is an unconvincing way to get the Born rule, is cooked that way. Also to be fair, that pdf is not exactly Carroll's. He does not call them pseudo-branches, here is Carroll's take (see section 3.2):

https://arxiv.org/pdf/1405.7577.pdf

 

[kered rettop]

The argument you are making here has been made in the literature by multiple people, going back, IIRC, some decades. I am not the only one who is not convinced by it. In any case, it is not something we are going to resolve here. Putting the various viewpoints on record here is fine, but we should not expect to actually reach a resolution when the community as a whole has not done so despite discussing this for far longer than we have here.

It would be nice to know why they cannot reach consensus though. Perhaps someone should start a thread on it.

 

[PeterDonis]

It's still there!

Not the post where you used the words "SEP definition" and then cut it off. That's been deleted.

If there is some other post you meant, please give me its number.

 

[PeterDonis]

It would be nice to know why they cannot reach consensus though.

I don't think there is even consensus on that. That can be expected to happen when you are dealing with questions that cannot be resolved by experiment, in a domain where what can be resolved by experiment is highly counterintuitive and is known not to have any simple resolution that meets our natural classical expectation.

 

[jbergman]

For me it's relatively straightforward. In the MWI there is a branching into "worlds" where a world is isolated from the other worlds that make up the wavefunction.

Then the probability of something happening or being observed after measurement is literally just,

# of worlds with outcome A / total # of worlds.

The harder part is to pin down what exactly are the worlds.

 

[kered rettop]

I don't think there is even consensus on that.

So it would seem, assuming PF users are representative. Still, putative explanations and meta-explanations do shed some light on the physics issues even if the reason for there being no consensus remains a mystery.

 

[PeterDonis]

In the MWI there is a branching into "worlds" where a world is isolated from the other worlds that make up the wavefunction.

Yes.

Then the probability of something happening or being observed after measurement is literally just,

# of worlds with outcome A / total # of worlds.

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is $1$. It doesn't matter what the weight of that particular outcome is, since that weight makes no difference to whether the outcome happens or not. It always happens as long as there is any nonzero weight at all.

In any particular world, you can formulate a notion of "probability" of something happening based on its relative frequency in that world. But that's not the same thing as the ratio you give. This is one of the key issues with formulating a concept of probability in the MWI, and has been discussed in the literature for decades with no resolution.

 

[pines-demon]

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is $1$. It doesn't matter what the weight of that particular outcome is, since that weight makes no difference to whether the outcome happens or not. It always happens as long as there is any nonzero weight at all.

In any particular world, you can formulate a notion of "probability" of something happening based on its relative frequency in that world. But that's not the same thing as the ratio you give. This is one of the key issues with formulating a concept of probability in the MWI, and has been discussed in the literature for decades with no resolution.

We have discussed it and I see how it could be a definitional issue, but is it a point of non-consensus though? Does criticism in literature centers about this? Clearly this is no point of conflict between MWI advocates so I guess it is brought by detractors?

 

[PeterDonis]

is it a point of non-consensus though? Does criticism in literature centers about this?

It is one of multiple points that are not resolved in the literature.

Clearly this is no point of conflict between MWI advocates

Yes, it is. That's part of the problem: even MWI advocates don't all agree on these questions.

 

[PeterDonis]

either Carroll isn't doing that

As far as I can tell from Carroll's "self-locating uncertainty" paper, he isn't. His approach there is different.

 

[pines-demon]

It is one of multiple points that are not resolved in the literature.


Yes, it is. That's part of the problem: even MWI advocates don't all agree on these questions.

Could you provide some sources about this criticism? From what I can read from Wikipedia or Carroll's differences between MWI proposals are not based at all on the problem of branch counting being an issue. What seems to matter is if their respective ways of counting really derive the Born rule or not.

 

[gentzen]

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is $1$.

is it a point of non-consensus though?

It is one of multiple points that are not resolved in the literature.

Clearly this is no point of conflict between MWI advocates

Yes, it is. That's part of the problem: even MWI advocates don't all agree on these questions.

Can you provide a quote from any MWI advocate saying that "the probability of any outcome with a nonzero amplitude in the wave function happening is $1$"? Why should a MWI advocate use the word "probability" in that way?

 

[PeterDonis]

Could you provide some sources about this criticism.

I think some have already been given in this thread, in the form of papers by different MWI proponents saying different, incompatible things.

 

[PeterDonis]

Can you provide a quote from any MWI advocate saying that "the probability of any outcome with a nonzero amplitude in the wave function happening is $1$"?

Of course not, because MWI advocates, when they discuss this aspect at all, avoid pointing out the obvious fact that all outcomes happen in the MWI. They avoid pointing it out precisely because it would invite the reader to make the observation I made, and that would undermine MWI advocates' attempts to formulate a meaningful concept of probability. At least, that's my skeptical take on it. If you want an MWI advocate's take on it, you would need to ask them: but ask them how the probability of any outcome can be anything except $1$ when the MWI says all outcomes are guaranteed to happen.

 

[pines-demon]

I think some have already been given in this thread, in the form of papers by different MWI proponents saying different, incompatible things.

Sure but being incompatible does not mean that they are being incompatible due to your argument.

I sincerely think that we either need to dig into the sources or let this thread end. I am no longer even sure that the question of the thread is justified by the sources.

 

[pines-demon]

Of course not, because MWI advocates, when they discuss this aspect at all, avoid pointing out the obvious fact that all outcomes happen in the MWI. They avoid pointing it out precisely because it would invite the reader to make the observation I made, and that would undermine MWI advocates' attempts to formulate a meaningful concept of probability. At least, that's my skeptical take on it. If you want an MWI advocate's take on it, you would need to ask them: but ask them how the probability of any outcome can be anything except $1$ when the MWI says all outcomes are guaranteed to happen.

Usually good academic papers tend to point out the different arguments against them. Carroll's does that but not this point in specific. Maybe that argument is found elsewhere in critics of MWI.

 

[PeterDonis]

dig into the sources

As I have commented before, the sources go back decades. The ones dating from before decoherence theory was developed are less useful because they don't take that into account. But even the ones since still cover at least 3 decades. There is a lot of literature on this topic.

 

[jbergman]

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is $1$. It doesn't matter what the weight of that particular outcome is, since that weight makes no difference to whether the outcome happens or not. It always happens as long as there is any nonzero weight at all.

Sure, everything happens. But I don't think that invalidates the probability definition I gave.

You can think of it likes this. Each observer after measurement, will only be able to see the outcome in their world. So the probability measures the fraction of observers who will experience outcome A. It's not that complicated.

The much harder part is to move from equal probability situations to unequal ones.

 

[PeterDonis]

everything happens. But I don't think that invalidates the probability definition I gave.

And there are MWI proponents who agree with you. But there are also ones who don't. And of course there are plenty of MWI skeptics (including me) who don't. So, as with anything to do with QM interpretations, this comes down to a difference of opinion. Neither side can convince the other because there is no way to settle the question by experiment: both sides make the same predictions for all experimental results.

 

[jbergman]

Sure but being incompatible does not mean that they are being incompatible due to your argument.

I sincerely think that we either need to dig into the sources or let this thread end. I am no longer even sure that the question of the thread is justified by the sources.

Agree. I think most accept the definition of probability in Many Worlds. David Albert is one I know who objects, though.

 

[PeterDonis]

Each observer after measurement, will only be able to see the outcome in their world.

Yes.

So the probability measures the fraction of observers who will experience outcome A.

But no observer can ever measure this. So on this view nobody ever measures the probability of outcome A. Which makes this definition useless.

 

[jbergman]

And you will find MWI proponents who agree with you. But there are also ones who don't. And of course there are plenty of MWI skeptics (including me) who don't. So, as with anything to do with QM interpretations, this comes down to a difference of opinion. Neither side can convince the other because there is no way to settle the question by experiment: both sides make the same predictions for all experimental results.

I consider myself and MWI skeptic but for different reasons. I don't understand a physical justification for the measure assigned to worlds for the exact reasons you brought up before, i.e. what is the justification of introducing additional state to give the needed number of worlds to get the right probabilities.

 

[jbergman]

But no observer can ever measure this. So on this view nobody ever measures the probability of outcome A. Which makes this definition useless.

You can measure by making multiple measurements under the assumption your world assignment is random.

 

[gentzen]

It makes it clear that you don't intent to give references which support your claim. What is still unclear is whether you intent to give reasons or arguments for your claim beyond "(and rather obviously so)".

Lighten up! You asked for an opinion about your own inference about my personal view. I opined that it was probably valid. That means nothing more than I think you have correctly understood me.

I am simply pointing out that saying "and rather obviously so" without any supporting arguments is a bit disappointing in a discussion like this.

To remind you: I claimed that a world-counting argument to derive probabilities is only valid if the worlds have equal probabilities a priori. I am not sure what sort of reference would back that up. Perhaps a link to a Wiki article about logical thinking?

Your logical thinking is fine, but your rhetorics (the art of persuasion) has room for improvement.
So your argument is that the principle of indifference cannot be applied in cases where there obviously is a difference. This seems to be a good argument against some of the misguided stuff that came up during this discussion. I think you (or someone else) made that argument before, and I liked that post. But apparently not, because I am unable to find that post again.

I was hoping for a simple convincing argument why trying to reduce all probabilities in MWI to the case of equal probabilities is misguided. My argument was an elaboration of my reaction to your disagreement with Peter Donis about "nonzero amplitude" for flying pigs

I've already told you: I don't think the wave function has a nonzero amplitude for what you're claiming. It's up to you to show that it does, since you are the one that made the claim about flying pigs. You have already agreed with me that a nonzero amplitude in the wave function for such a transition is necessary to support your claim. So it's up to you to show that in fact such a nonzero amplitude exists. You can't just assume that there is a nonzero amplitude for anything you like.

namely that focusing on "nonzero" vs "exactly zero" is not a robust way to look at things.

Which counting arguments? Some are obviously wrong, others appear to be perfectly valid.

The counting arguments which try to reduce all probabilities in MWI to the case of equal probabilities.

You see, I had hoped for a "MWI proponent" that could engage in discussions like

Of course not, because MWI advocates, when they discuss this aspect at all, avoid pointing out the obvious fact that all outcomes happen in the MWI. They avoid pointing it out precisely because it would invite the reader to make the observation I made, and that would undermine MWI advocates' attempts to formulate a meaningful concept of probability. At least, that's my skeptical take on it.

and come up with convincing arguments for the MWI side. My arguments go along the line of "do you have a reference for this?", but of course that is normally hardly convincing.

 

[kered rettop]

I sincerely think that we either need to dig into the sources or let this thread end. I am no longer even sure that the question of the thread is justified by the sources.

The fact that you have cluttered up the thread with inconclusive side-issues, doesn't mean it should be closed. If anyone has the right get it closed it would be the OP, viz me. Please recall that as soon as PeterDonis answered, I said I wanted to digest his answer properly before answering. I haven't done so yet but as far as know there is no forum requirement to do so within a time limit measured in days. Isn't the subject difficult enough without having people trying to veto it? If you want to terminate your off-topic subthread, feel free, but please don't try to scupper my attempt to understand the issue.

 

[pines-demon]

The fact that you have cluttered up the thread with inconclusive side-issues, doesn't mean it should be closed.

If you want to terminate your off-topic subthread, feel free, but please don't try to scupper my attempt to understand the issue.

Which side-issues? I have tried to stay on topic.

If anyone has the right get it closed it would be the OP, viz me. Please recall that as soon as PeterDonis answered, I said I wanted to digest his answer properly before answering. I haven't done so yet but as far as know there is no forum requirement to do so within a time limit measured in days. Isn't the subject difficult enough without having people trying to veto it?

I agree, please be free to continue the discussion or specify what you are not getting. I just feel that we are repeating the same arguments.

As the OP why do you think there is no consensus on the meaning of probability in MWI? What made you think that? What do you mean by "meaning"? Is it that people define different probabilities? or is it that nobody can agree that even probabilities can be made? By consensus, you mean consensus between MWI advocates or all physicists?

Sources on that problem/motivation are welcome.
Edit: to be clear I said dig into the sources or end it, but it was mostly to motivate the former not the latter

 

[PeterDonis]

You can measure by making multiple measurements under the assumption your world assignment is random.

But your world assignment isn't random. It is determined by the sequence of measurement results you observe, and each measurement deterministically produces all possible results. There is no randomness anywhere. Once you specify what measurements are to be made and in what order, you have completely specified what is in every resulting world. There is no room for any random selection.

 

[PeterDonis]

focusing on "nonzero" vs "exactly zero" is not a robust way to look at things

We don't have to consider any of the outlandish cases you mention, where this becomes an issue. Even if we just limit ourselves to measurements on qubits where there are finite but unequal weights (say 1/3 and 2/3), all of the issues we are discussing are already in play.

 

[PeterDonis]

there is no forum requirement to do so within a time limit measured in days

That is correct.

 

[pines-demon]

Agree. I think most accept the definition of probability in Many Worlds. David Albert is one I know who objects, though.

Can you provide a source or comment on his view? this might help the conversation.

 

[gentzen]

We don't have to consider any of the outlandish cases you mention, where this becomes an issue. Even if we just limit ourselves to measurements on qubits where there are finite but unequal weights (say 1/3 and 2/3), all of the issues we are discussing are already in play.

Do you have a "simple convincing argument why trying to reduce all probabilities in MWI to the case of equal probabilities is misguided"? My argument (for why this is misguided) doesn't work at all for simple fractions like 1/3 and 2/3, and would not be very convincing for "nearly" simple fractions like (1+ϵ)/3 and (2-ϵ)/3. That is why I focused on the outlandish cases.